# The mathematical work of John Napier (1550-1617). (Volumes I-III)

Abstract (Summary)

John Napier, born at Merchiston in 1550, published The Whole Revelation of St. John in 1594; and he appears to have regarded that theological polemic as his most important achievement. Napier's invention of logarithms (with greatly advanced spherical trigonometry) was published in 1614 as Descriptio Canonis Logarithmorum; whereupon the mathematicians of Europe instantly acclaimed Napier as the greatest of them all. In 1617 he published Rabdologiae, which explained several devices for aiding calculation: (1) numbering rods to aid multiplication (known as 'Napier's bones'); (2) other rods to aid evaluation of square and cube roots; (3) the first publication of binary arithmetic, as far as square root extraction; and (4) the Promptuary for multiplication of numbers (up to 10 digits each), which has a strong claim to be regarded as the first calculating machine. Napier's explanation of the construction of his logarithms was published posthumously in 1619 as Constructio Canonis Logarithmorum, in which he developed much of the differential calculus in order to define his logarithms as the solution of a differential equation and then constructed strict upper and lower bounds for the solution. His incomplete manuscript on arithmetic and algebra (written in the early 1590s) was published in 1839 as De Arte Logistica. This thesis provides the first English translations of De Arte Logistica and of Rabdologiae, and it reprints Edward Wright's English translation (1616) of the Descriptio and W. R. Macdonald's English translation (1889) of the Constructio. Extensive commentaries are given on Napier's work on arithmetic, algebra, trigonometry and logarithms. The history of trigonometry is traced from ancient Babylonia and Greece through mediaeval Islam to Renaissance Europe. Napier's logarithms (and spherical trigonometry) resulted in an explosion of logarithms over most of the world, with European ships using logarithms for navigation as far as Japan by 1640.
Bibliographical Information:

Advisor:

School:The University of Auckland / Te Whare Wananga o Tamaki Makaurau

School Location:New Zealand

Source Type:Master's Thesis

Keywords:mathematics 0405 history of science 0585

ISBN:

Date of Publication:01/01/1982